Suppose a time sequence of networks is observed. It is known that the probabilistic behaviors of the networks do not change over time, except at a few time points. These time points are usually called change points, whose number and locations are unknown. This paper proposes a method for automatically estimating such change points and the community structures of the networks. The proposed method invokes the minimum description length principle to derive a model selection criterion, where the best estimates are defined as its minimizer. It is shown that this selection criterion yields consistent estimates for the change points as well as the community structures. For practical minimization of the selection criterion, a bottom-up search algorithm that combines the EM-algorithm with variational approximation is developed. The promising empirical properties of the proposed method are illustrated via a sequence of numerical experiments and applications to some real datasets. To the best of the authors’ knowledge, this method is one of the earliest that provides consistent estimates in the context of change point detection for time-evolving networks.

中文翻译：

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时间演化动态网络中变化点检测和社区估计的统计一致性


假设观察到网络的时间序列。众所周知，除了少数时间点外，网络的概率行为不会随时间变化。这些时间点通常称为变化点，其数量和位置未知。本文提出了一种自动估计此类变化点和网络社区结构的方法。所提出的方法调用最小描述长度原则来导出模型选择标准，其中最佳估计被定义为其最小值。结果表明，该选择标准对变化点以及群落结构产生一致的估计。为了实际最小化选择标准，开发了一种将 EM 算法与变分近似相结合的自下而上搜索算法。通过一系列数值实验和对一些真实数据集的应用，说明了所提出方法的有希望的经验特性。据作者所知，该方法是最早在时间演化网络的变化点检测中提供一致估计的方法之一。